Two engineers are discussing if typical 100 psig compressed air used in a pneuma

Question

Two engineers are discussing if typical 100 psig compressed air used in a pneumatic driven and controlled manufacturing operation can be considered an ideal gas and, therefore, allows them to use the ideal gas law. You can assist them by referencing the compressibility factor “Z”. Use the compressibility factor Z and the information from Figure A-1 (of our course textbook) to quantitatively and computationally justify if the 100 psig shop air can, or cannot, be considered an ideal gas. (Recall that for many applications values of “Z” within the range of 0.97 to 1.03 could easily allow the use of the ideal gas law with few problems and little error.) Two engineers are discussing if typical 100 psig compressed air used in a pneumatic driven and controlled manufacturing operation can be considered an ideal gas and, therefore, allows them to use the ideal gas law. You can assist them by referencing the compressibility factor “Z”. Use the compressibility factor Z and the information from Figure A-1 (of our course textbook) to quantitatively and computationally justify if the 100 psig shop air can, or cannot, be considered an ideal gas. (Recall that for many applications values of “Z” within the range of 0.97 to 1.03 could easily allow the use of the ideal gas law with few problems and little error.)

Explanation / Answer

now, given pressure, P = 100 Psig = 689476 Pa
now ideal gas equation is givne by
PV = nRT
and Z factor is given by
PV/nRT = Z
so for Z = 1, the gas is ideal in nature otherwise it is not
Now, from the website peacesoftware.de which helps calculating z factor of gases online, Z factor of compressed air at this pressure and 300 K is
Z = 0.99802
this value is very close to 1, hence air at this pressure temperature can be considered to be ideal gas

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